A Mathematical Formulation of Control Problems on Cognitive Models

Abstract. This paper considers cognitive modeling methods under different types of control. Relevant publications are briefly surveyed. The cognitive model is formally described as a simulation model based on a directed graph (signed or weighted digraph). Mathematical formulations of the optimal, conflict, and hierarchical control problems are proposed for cognitive models in the case of pulse processes and in the general case as well. The methodology is applied to the predator-prey model and the aggregative model of a national economy. The methodological assumptions are detailed for another control problem on a cognitive map (the optimal management of a university). In this model, a university determines the number of commercial places and the price of commercial education. The model is identified on real data for the three largest universities of the Rostov region (the Russian Federation). Some conclusions and recommendations are formulated based on model analysis.

Keywords: control problems, discrete dynamic models, cognitive modeling, control in social and economic systems.